Concrete, Representational, Abstract (CRA) is a 3 phase instructional approach for teaching math. I have been personally using this approach to guide my instruction and have found it extremely beneficial to my students.
The first stage of the CRA approach is called Concrete. In this stage, students are learning and exploring a math concept solely with manipulatives. For instance, if a student were learning about adding numbers by place value, they may use Base 10 blocks as a tool. In the concrete stage, the student would be solving the addition problem by representing the numbers with Base 10 blocks and then combining the blocks to add. The student would investigate regrouping by exchanging 10 ones blocks for a ten block or ten tens blocks for one hundred block. The purpose of the Concrete stage is for student to build their conceptual understanding of a math concept.
In the second stage, Representational, the concrete manipulatives are connected to pictures and drawings. The connection between the two stages is essential. In the previous example, students used Base 10 blocks to add numbers and regroup. In the Representational stage, students will draw pictures of the Base 10 blocks and use notation such as circling and crossing off to represent regrouping.
Finally, is the Abstract stage. In this stage, students connect the work they did in the Concrete and Representational stages to the Abstract numbers. In this stage, students would be solving an addition problem by lining up the digits by place value and solving using the standard algorithm.
Our end goal in teaching our students using the CRA method is to get them working in the Abstract stage. I would not want a grown adult to have to solve an addition problem using Base 10 Blocks or even drawing a pictures. However, the transition from Concrete, to Representational to Abstract and the connections made between the stages is what gives students the deep conceptual understanding they need.
Following this approach for teaching math has been life changing for me. If the CRA approach is something you are interested in, please follow me at Math Hands On. We will be exploring math concepts following this approach, deepening math understanding one lesson at a time. 🙂